De Boer was dismissed after only 77 days in the job – the shortest reign in Premier League history – and losing all four of his first four games, scoring no goals in the process.
Roy Hodgson is expected to be named his successor on Tuesday but Allardyce, appearing on Sky Sports’ Monday Night Football, revealed he was contacted by Parish, despite resigning from the Selhurst Park managerial role at the end of last season.
He said: “Just to make it clear, to stop speculation, I spoke to Steve [Parish] before I got here and I said I wouldn't feel comfortable at this moment in time taking any position as a football manager.
“I'm enjoying my life too much without the pressures of the Premier League. He didn't offer me the job but asked me what my thoughts were.
“It was a clever question and I told him what I was thinking and that if they were to offer me the job, at this moment in time I wouldn't want to go back.
“There's certainly huge pressure, more pressure than ever, in the Premier League as we've seen by Frank going so early.”
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